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In: Advanced Math

Systems of Ordinary Differential Equations

Let A be a square matrix defined by

(a) Find the eigenvalues and eigenspaces of A.

(b) Show that A is not diagonalizable but triangularizable. Triangularize A.

Solutions

Expert Solution

Solution

(a) Find the eigenvalues and eigenspaces of A.

Find the eigenspaces associated to eigenvalues

Therefore, the eigspace associated with

(b) Show that A is not diagonalizable but triangularizable. Triangularize A.

Therefore, A is not diagnoalizable, but triangularizable

The solution of system x'(t)=A x(t) is

Then the solution to x(t) is

Then, solve the initial value problem x'(t)=Ax(t)+B(t)

Determine the constants of particular solution first where\

SUN BUNRA answered 1 year ago

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